No.

Casting either of those spells requires that you use your Action to Cast a Spell, even though the spell lets you make a melee attack with your weapon.

Extra Attack is only triggered when you take the Attack Action. There are several examples of Extra Attack in the PHB, so here's the one from Fighter in the PHB pg. 72, emphasis mine:

Extra Attack

Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.

Green Flame Blade and Booming Blade are both cantrips, which are covered under spellcasting rules. More importantly, both of them have a requirement of using 1 Action to be cast, and the melee attack is part of the spell.